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摘要
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms [Parity in knot theory, Sb. Math. 201 (2010) 693-733] to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of the odd writhe polynomial defined by the first author in [A polynomial invariant of virtual knots, preprint (2012), arXiv:math.GT/1202.3850v1]. The relation between this new polynomial invariant and the affine index polynomial [An affine index polynomial invariant of virtual knots, J. Knot Theory Ramification 22 (2013) 1340007; A linking number definition of the affine index polynomial and applications, preprint (2012), arXiv:1211.1747v1] is discussed. In the second part we introduce a polynomial invariant for long flat virtual knots. In the third part we define a polynomial invariant for 2-component virtual links. This polynomial invariant can be regarded as a generalization of the linking number.
- 出版日期2013-10
- 单位北京师范大学
